Matrix row and column operations

acron shared this idea 9 years ago

I would like to see some of the following Matrix Row commands

• SwapRows[matrix,row1,row2] swap row1 with row2

MultiplyRow[scalar, matrix, row] multiplies matrix by scalar and stores in row

MultiplyRowAdd[<scalar>,<matrix>,<row1>,<row2>] multiply row1 by scalar add to row2 and store in row2

EliminateCol[<matrix>,<scalar1>,<row1>,<scalar2>,<row2>] multiply scalar1 by row 1 and add to scalar2 by row2, storing result in row2

These commands would shorten the creation of applets such as this: Gauss-Jordan Elimination

This lesson was created to assist students to do the Row operations needed to solve matrices without tech...technology is not appreciated without understanding the simple lessons we all learned...

Tony

A better example is this lesson 2x2 Elimination

1

+1

Would be useful for Simplex Algorithm modelling, for Linear Programming too. (I guess the spreadsheet could be used for this)

K.

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Would be useful for Simplex Algorithm modelling, for Linear Programming too. (I guess the spreadsheet could be used for this)

K.

both my examples used this, but the organization on the second in much better...

Thanks for the vote of support...

Tony

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I would find these commands immediately useful as I continue to develop 3D GeoGebra based software for my NSF TUES Grant (Award ID: 1141045) entitled Transforming Linear Algebra Education with GeoGebra Applets.

In general, they would be very valuable for anyone using GeoGebra to teach linear algebra.

Jim

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The 5 personal tools tried by hand (EliminateRow or EliminateCol ?). Cheers. Michel.

https://ggbm.at/567429

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Thanks, miir, for a nice job in making these tool. The more advanced users will appreciate this greatly, especially when add to the list of tools available on GGT.

However, most novice users who find the matrix tools in the GeoGebra list of commands, will not know how to access the GGT tools available and will find GeoGebra lacking in the built-in commands; they may look elsewhere for a matrix solving tool. A tool which has them build-in to the OS already. I hope the developers will keep this in mind as additional commands to add into the native mode...

One suggestion for th Input Help menu under Vector & Matrix, add link to these tools until such time as the tool is added to the OS...I know it takes time to work on new subroutines and modules.

Thanks for the great work...

Tony

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I don't see the pedagogic point - shouldn't Matrix Algebra should be illustrated with Matrix Algebra operations: Additions, Multiplications

the computer is really good at printing out stuff that was too "verbose", highly redundant to hand write - like the matrixes that swap, scale, add, subtract rows, columns

perhaps the easy to "see" human heuristic labels are helpful shortcuts - but I would put the matrixes that do the work on the screen - maybe the idea of matrix multiplication, composition of products, the extension of "Algebra" to Matrixes will sink in

the index manipulation in the example code/function defs seems like something to discourage at a introductory level where getting fundamental principles across is more important then algorithmic efficiency

1

I don't see the pedagogic point - shouldn't Matrix Algebra should be illustrated with Matrix Algebra operations: Additions, Multiplications

the computer is really good at printing out stuff that was too "verbose", highly redundant to hand write - like the matrixes that swap, scale, add, subtract rows, columns

Matrix Algebra is illustrated with many simple operations, most matrix lessons in education today, seldom go beyond learning a 3x3 matrix by hand...when a class can handle all of the matrix operations easily, technology devices can manage tedious hours of intense, detailed operations in a few seconds...Have you ever had to solve a 5x6 matrix for the five variables...determined the inverse matrix of a 12 x 12matrix? Many problem require the ability to be able to do such problems quickly and easily...BTW in 1968-1969 I was doing similar problems in my undergrad work...when you do a problem which takes two hours you really appreciate doing it is a few seconds...we are trying to not have the computer printout the verbose matrices...I am looking for the simple final solution which these provide...

Tony

1

certainly you want inverse, transpose, LU decomposition... all as high level functions

the row/column swap functions however are for implementing algorithms like Gaussian Elimination - my question is where is/is this important in teaching Matrix Algebra

I would much rather see the Vector Exterior product which clarifies Determinants, makes Cramer's Rule become a teachable exercise in Algebra instead of a mass of weird definitions and unmotivated rules

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Vector Exterior product

Please post a reference for what that is and an example of why it's useful :)

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... Sometimes in Italy the cross product (vector product) is also named external product - if this helps ;)

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Vector Exterior Products may require a Geogebra 6 with a refactoring for “Geometric Algebra” Real Clifford Algebra containing the Grassman Exterior Product

for the specific use of Grassman/Clifford Exterior Vector Product in Linear Algebra: http://en.wikipedia.org/wik... shows the “Geometric” version, and the Clifford Algebra version with the exterior “wedge” product is essentially Hestenes “Geometic Algebra”

The Vector Exterior/Outer/Wedge product is “behind” the cross product

for Linear Algebra we want to go beyond just the 3D version of Geometric Algebra that is good for intro physics, fortunately GA “scales” smoothly – where Gibbs/Heaviside is stuck in 3D – and which may explain why the GA view of Linear Algebra is also so late in recognition, use in elementary classes

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To facilitate explanation of linear algebra, also come very well two simple commands:

• GetRow [<matrix>, <integer>]

GetColumn [<matrix>, <integer>]

Rafa

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hola Rafa

GetRow [<matrix>, <integer>] equal to {Element[<matrix>, <integer>]}

saludos

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Hi, Mathmagic. I know, but for the student, direct commands for each row and column are more intuitive. Is not it?

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Rafa, I totally agree with you, this is why I started this...hopefully, this will become a future path...

Tony

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not a teacher, but curious about these requests

are you teaching Matrix Algebra or "visual algorithms" - just smoothing over, accepting historical practice or developing/advancing pedagogy with the computer

is it the "right" intuition if its disconnected from Matrix Multiplication, doesn't keep up front the ideas of composing the operations of Gaussian elimination by multiplying, adding up the many row/column swapping elementary matrix operations in the Gaussian Elimination Algorithm?

why avoid using the computer to Display the too tedious to hand write full matrix multiplication steps

how about displaying a palette of elementary row/column operation matrixes, require clicking on each to add to the operands on each side of the equation

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I hope I can satisfy your curiosity, we are teaching introductory Matrix Operations usually from the classical sense. Most students are never going to become daily users matrix algebra mathematics, but if someone has a basic understanding of the process they will know mathematics can be used in amazing ways. As a continuous user of matrix operations, the nice matrix commands such as RowEchelonForm and ReduceRowEchelonForm save a lot of time and effort...there are even nicer forms which the matrix algebraist use, which to the beginning student are impossible to understand.

It is my understanding GeoGebra is supposed to be a Dynamic Mathematics for Everyone. The advanced matrix tools are not really for everyone, the simpler tools are needed for those of us training future mathematicians. Our students sometimes can barely understand the concept of adding two 2x2 matrices. They need to gain an understanding as to what is going on. I can teach a student who can barely add single digit integers some neat ways to solve a 3x3 system of equations successfully but we would like some tools to assist them in learning matrix operations with row and columns...While for many who write here, mathematics was an easy task; out students struggle with concepts. Any tool which can make this easier for these students is needed within GG, IMHO...This is the reasoning I use when posting many of my requests...I am not a mathematical genius, I plod along trying to help students understand the beauty of mathematics...

GeoGebra does a good job assisting me in many areas, one of the weaker areas is with basic matrix operations (operations a good mathematician can accomplish mentally)...however, my students sometimes struggle learning...I will use the tools which get the job done; GeoGebra has been the best tool I have ever used in over 40 years of teaching...

I hope my points are persuasive...GeoGebra should help the weak as well as the strong student mathematician...

Tony